Question: The $n\text{th}$ partial sum of the series $\sum\limits_{n=1}^{\infty }{{{a}_{n}}}$ is given by ${{S}_{n}}=\frac{n-1}{n+1}$. $a_3=$
Explanation: ${{a}_{3}}={{S}_{3}}-{{S}_{2}}$ ${{a}_{3}}=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$